GAM evaluation - St. Lucie Estuary
Marcus Beck
Observed data
Observed log-chlorophyll at representative station for the St. Lucie Estuary
library(tidyverse)
library(lubridate)
library(mgcv)
library(plotly)
library(WRTDStidal)
library(gridExtra)
source('R/funcs.R')
# flow data, left moving window average of 30 days
data(sl_fldat)
fl_dat <- sl_fldat %>%
rename(date = Date) %>%
mutate(
qsm = stats::filter(q, rep(1, 30)/30, sides = 1, method = 'convolution')
)
# format the data to model
data(sl_dat)
sl_mod <- sl_dat %>%
rename(date = Date) %>%
mutate(
doy = yday(date),
dec_time = decimal_date(date),
yr = year(date),
yr = factor(yr),
mo = month(date, label = T)
) %>%
left_join(fl_dat, by = 'date') %>%
mutate(
flo = log(qsm),
chl = log(1 + chl)
) %>%
select(-q, -qsm, -sal)
# plot, all
p <- ggplot(sl_mod, aes(x = date, y = chl)) +
geom_line() +
theme_bw()
ggplotly(p)# boxplot, by years
p <- ggplot(sl_mod, aes(x = yr, y = chl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)# boxplot, by month
p <- ggplot(sl_mod, aes(x = mo, y = chl)) +
geom_boxplot() +
theme_bw()
ggplotly(p)GAMs with annual, seasonal trends
Some simple GAMs to explore annual, seasonal trends.
# smooths to evaluate
smths <- c(
"s(dec_time, bs = 'tp')",
"s(doy, bs = 'cc')",
"te(dec_time, doy, bs = c('tp', 'cc'))"
)
# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
frm <- combn(smths, i) %>%
apply(2, function(x){
paste(x, collapse = ' + ') %>%
paste('chl ~ ', .) %>%
formula
})
frms <- c(frms, frm)
}
# create models from smooth formula combinations
mods <- map(frms, function(frm){
gam(frm,
knots = list(doy = c(1, 366)),
data = sl_mod,
na.action = na.exclude
)
})
names(mods) <- paste0('mod', seq_along(mods))Summary stats of annual, seasonal models:
# smoother stats of GAMs
map(mods, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| mod1 | s(dec_time) | 1.49 | 1.83 | 8.05 | 0.00 |
| mod2 | s(doy) | 4.21 | 8.00 | 6.52 | 0.00 |
| mod3 | te(dec_time,doy) | 8.43 | 11.10 | 5.17 | 0.00 |
| mod4 | s(dec_time) | 1.88 | 2.35 | 6.03 | 0.00 |
| mod4 | s(doy) | 4.22 | 8.00 | 6.63 | 0.00 |
| mod5 | s(dec_time) | 1.00 | 1.00 | 5.66 | 0.02 |
| mod5 | te(dec_time,doy) | 9.56 | 15.00 | 3.33 | 0.00 |
| mod6 | s(doy) | 4.21 | 8.00 | 5.84 | 0.00 |
| mod6 | te(dec_time,doy) | 2.74 | 3.81 | 4.00 | 0.00 |
| mod7 | s(dec_time) | 1.00 | 1.00 | 10.64 | 0.00 |
| mod7 | s(doy) | 4.16 | 8.00 | 5.16 | 0.00 |
| mod7 | te(dec_time,doy) | 2.85 | 15.00 | 0.28 | 0.16 |
# summary stats of GAMs
map(mods, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | AIC | R2 |
|---|---|---|
| mod1 | 654.57 | 0.04 |
| mod2 | 621.13 | 0.13 |
| mod3 | 619.47 | 0.15 |
| mod4 | 609.37 | 0.16 |
| mod5 | 619.10 | 0.15 |
| mod6 | 609.19 | 0.17 |
| mod7 | 608.68 | 0.17 |
# prediction data
pred_dat <- crossing(
yr = seq(floor(min(sl_mod$dec_time)), ceiling(max(sl_mod$dec_time))),
doy = seq(1, 365, by = 5)
) %>%
unite('date', yr, doy, sep = '-', remove = F) %>%
mutate(
date = as.Date(date, format = '%Y-%j'),
dec_time = decimal_date(date),
mo = month(date, label = TRUE),
yr = year(date)
) %>%
left_join(., fl_dat[, c('date', 'qsm')]) %>%
mutate(flo = log(qsm)) %>%
select(-qsm)
# predictions
sl_res <- map(mods, function(x){
pred_dat %>%
mutate(
pred = predict(x, newdata = pred_dat)
)
}) %>%
enframe('mods') %>%
unnest
# plot
p <- ggplot(sl_res, aes(x = date)) +
geom_point(data = sl_mod, aes(y = chl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)# plot
p <- ggplot(sl_res, aes(x = doy, group = factor(yr), colour = yr)) +
geom_line(aes(y = pred)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
) +
facet_wrap(~ mods, ncol = 2)
ggplotly(p)GAMs with annual, seasonal, and flow trends
Adding flow data to the model:
# smooths to evaluate
smths <- c(
"s(dec_time, bs = 'tp')",
"s(doy, bs = 'cc')",
"s(flo, bs = 'tp')",
"te(flo, doy, bs = c('tp', 'cc'))",
"te(flo, dec_time, bs = c('tp', 'tp'))",
"te(dec_time, doy, bs = c('tp', 'cc'))",
"te(dec_time, doy, flo, bs = c('tp', 'cc', 'tp'))"
)
# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
frm <- combn(smths, i) %>%
apply(2, function(x){
paste(x, collapse = ' + ') %>%
paste('chl ~ ', .) %>%
formula
})
frms <- c(frms, frm)
}
# create models from smooth formula combinations
mods2 <- map(frms, function(frm){
gam(frm,
knots = list(doy = c(1, 366)),
data = sl_mod,
na.action = na.exclude
)
})
names(mods2) <- paste0('mod', seq_along(mods2))
save(mods2, file = 'data/sl_mods2.RData', compress = 'xz')Summary stats of best year/season model, year/season/flow model:
data(sl_mods2)
# best model with only season, year
best1 <- map(mods, ~ summary(.x)$r.sq) %>%
unlist %>%
which.max %>%
mods[[.]]
# best model with season, year, flow
best2 <- map(mods2, ~ summary(.x)$r.sq) %>%
unlist %>%
which.max %>%
mods2[[.]]
best <- list(best1 = best1, best2 = best2)
# smoother stats of GAMs
map(best, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| best1 | s(dec_time) | 1.00 | 1.00 | 10.64 | 0.00 |
| best1 | s(doy) | 4.16 | 8.00 | 5.16 | 0.00 |
| best1 | te(dec_time,doy) | 2.85 | 15.00 | 0.28 | 0.16 |
| best2 | s(dec_time) | 1.00 | 1.00 | 1.93 | 0.17 |
| best2 | s(doy) | 2.94 | 8.00 | 0.71 | 0.05 |
| best2 | s(flo) | 6.78 | 7.86 | 2.96 | 0.00 |
| best2 | te(flo,doy) | 2.96 | 12.00 | 0.58 | 0.01 |
| best2 | te(flo,dec_time) | 0.21 | 15.00 | 0.02 | 0.09 |
| best2 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.81 |
| best2 | te(dec_time,doy,flo) | 19.86 | 48.00 | 1.01 | 0.00 |
# summary stats of GAMs
map(best, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | AIC | R2 |
|---|---|---|
| best1 | 608.68 | 0.17 |
| best2 | 556.83 | 0.34 |
# predictions
sl_res2 <- map(best, function(x){
pred_dat %>%
mutate(
pred = predict(x, newdata = pred_dat)
)
}) %>%
enframe('mods') %>%
unnest
# plot
p <- ggplot(sl_res2, aes(x = date)) +
geom_point(data = sl_mod, aes(y = chl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)ptheme <- theme(
axis.title.x = element_blank(),
axis.title.y = element_blank()
)
cols <- 'Spectral'
pb1 <- dynagam(best1, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
theme(legend.position = 'none') +
ggtitle('Best 1')
pb2 <- dynagam(best2, pred_dat, ncol = 1, col_vec = cols) +
ptheme +
ggtitle('Best2')
pleg <- g_legend(pb2)
pb2 <- pb2 +
theme(legend.position = 'none')
grid.arrange(
pleg,
arrangeGrob(pb1, pb2, ncol = 2, bottom = 'lnQ', left = 'lnchl'),
ncol = 1,
heights = c(0.1, 1)
)
Adding nitrogen and turbidity covariates
# formula for best annual, seasonal, flow model
strt <- best2$formula %>%
as.character
smths <- c(
"s(nh, bs = 'tp')",
"s(tss, bs = 'tp')",
"te(nh, tss, bs = c('tp', 'tp'))"
)
# get all combinations of smoothers to model, one to many
frmstab <- list()
frms <- list()
for(i in seq_along(smths)){
# for the summary table
frmtab <- combn(smths, i) %>%
apply(2, function(x){
paste(x, collapse = ' + ')
})
# for the model
frm <- sapply(frmtab, function(x){
paste('chl ~', strt[3], '+', x) %>%
formula
})
frmstab <- c(frmstab, frmtab)
frms <- c(frms, frm)
}
# create models from smooth formula combinations
mods3 <- map(frms, function(frm){
gam(frm,
knots = list(doy = c(1, 366)),
data = sl_mod,
na.action = na.exclude
)
})
names(mods3) <- paste0('mod', seq_along(mods3))Summary of all nutrient, turbidity models
# smoother stats of GAMs
map(mods3, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| mod1 | s(dec_time) | 7.15 | 8.14 | 2.28 | 0.02 |
| mod1 | s(doy) | 4.43 | 8.00 | 4.71 | 0.00 |
| mod1 | s(flo) | 3.55 | 4.35 | 2.76 | 0.03 |
| mod1 | te(flo,doy) | 0.80 | 15.00 | 0.07 | 0.08 |
| mod1 | te(flo,dec_time) | 2.07 | 16.00 | 0.21 | 0.05 |
| mod1 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.66 |
| mod1 | te(dec_time,doy,flo) | 7.50 | 48.00 | 0.30 | 0.00 |
| mod1 | s(nh) | 3.11 | 3.79 | 8.77 | 0.00 |
| mod2 | s(dec_time) | 7.36 | 8.30 | 1.77 | 0.08 |
| mod2 | s(doy) | 3.73 | 8.00 | 2.14 | 0.00 |
| mod2 | s(flo) | 6.46 | 7.63 | 1.31 | 0.19 |
| mod2 | te(flo,doy) | 0.20 | 15.00 | 0.01 | 0.18 |
| mod2 | te(flo,dec_time) | 3.54 | 16.00 | 0.67 | 0.00 |
| mod2 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.62 |
| mod2 | te(dec_time,doy,flo) | 9.43 | 48.00 | 0.38 | 0.00 |
| mod2 | s(tss) | 4.01 | 4.92 | 3.55 | 0.00 |
| mod3 | s(dec_time) | 8.04 | 8.73 | 2.74 | 0.01 |
| mod3 | s(doy) | 4.41 | 8.00 | 5.71 | 0.00 |
| mod3 | s(flo) | 1.00 | 1.00 | 5.88 | 0.02 |
| mod3 | te(flo,doy) | 0.72 | 15.00 | 0.10 | 0.01 |
| mod3 | te(flo,dec_time) | 3.87 | 16.00 | 1.28 | 0.00 |
| mod3 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.59 |
| mod3 | te(dec_time,doy,flo) | 4.43 | 48.00 | 0.15 | 0.02 |
| mod3 | te(nh,tss) | 10.99 | 12.32 | 5.54 | 0.00 |
| mod4 | s(dec_time) | 7.87 | 8.63 | 2.28 | 0.02 |
| mod4 | s(doy) | 4.33 | 8.00 | 5.69 | 0.00 |
| mod4 | s(flo) | 4.66 | 5.69 | 2.82 | 0.01 |
| mod4 | te(flo,doy) | 0.03 | 15.00 | 0.00 | 0.10 |
| mod4 | te(flo,dec_time) | 2.70 | 16.00 | 0.36 | 0.01 |
| mod4 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.62 |
| mod4 | te(dec_time,doy,flo) | 6.09 | 48.00 | 0.23 | 0.01 |
| mod4 | s(nh) | 3.36 | 4.07 | 9.03 | 0.00 |
| mod4 | s(tss) | 4.52 | 5.49 | 3.83 | 0.00 |
| mod5 | s(dec_time) | 8.05 | 8.73 | 2.78 | 0.00 |
| mod5 | s(doy) | 4.40 | 8.00 | 5.36 | 0.00 |
| mod5 | s(flo) | 1.00 | 1.00 | 5.66 | 0.02 |
| mod5 | te(flo,doy) | 0.98 | 15.00 | 0.12 | 0.02 |
| mod5 | te(flo,dec_time) | 3.94 | 16.00 | 1.21 | 0.00 |
| mod5 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.60 |
| mod5 | te(dec_time,doy,flo) | 4.37 | 48.00 | 0.15 | 0.02 |
| mod5 | s(nh) | 3.62 | 4.51 | 5.90 | 0.00 |
| mod5 | te(nh,tss) | 9.82 | 20.00 | 1.52 | 0.00 |
| mod6 | s(dec_time) | 7.86 | 8.63 | 2.48 | 0.01 |
| mod6 | s(doy) | 4.24 | 8.00 | 5.00 | 0.00 |
| mod6 | s(flo) | 3.31 | 4.07 | 3.56 | 0.01 |
| mod6 | te(flo,doy) | 0.23 | 15.00 | 0.03 | 0.07 |
| mod6 | te(flo,dec_time) | 2.50 | 16.00 | 0.33 | 0.01 |
| mod6 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.62 |
| mod6 | te(dec_time,doy,flo) | 6.31 | 48.00 | 0.24 | 0.01 |
| mod6 | s(tss) | 4.60 | 5.58 | 3.60 | 0.00 |
| mod6 | te(nh,tss) | 2.25 | 14.00 | 2.78 | 0.00 |
| mod7 | s(dec_time) | 7.94 | 8.67 | 2.52 | 0.01 |
| mod7 | s(doy) | 4.34 | 8.00 | 4.73 | 0.00 |
| mod7 | s(flo) | 3.13 | 3.84 | 3.49 | 0.01 |
| mod7 | te(flo,doy) | 0.36 | 15.00 | 0.05 | 0.08 |
| mod7 | te(flo,dec_time) | 2.54 | 16.00 | 0.34 | 0.01 |
| mod7 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.64 |
| mod7 | te(dec_time,doy,flo) | 5.96 | 48.00 | 0.23 | 0.01 |
| mod7 | s(nh) | 1.00 | 1.00 | 0.01 | 0.93 |
| mod7 | s(tss) | 4.42 | 5.37 | 3.78 | 0.00 |
| mod7 | te(nh,tss) | 2.17 | 15.00 | 1.72 | 0.00 |
# summary stats of GAMs
map(mods3, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
mutate(smth_added = frmstab) %>%
select(name, smth_added, everything()) %>%
kable(digits = 2)| name | smth_added | AIC | R2 |
|---|---|---|---|
| mod1 | s(nh, bs = ‘tp’) | 497.81 | 0.37 |
| mod2 | s(tss, bs = ‘tp’) | 534.20 | 0.35 |
| mod3 | te(nh, tss, bs = c(‘tp’, ‘tp’)) | 481.66 | 0.41 |
| mod4 | s(nh, bs = ‘tp’) + s(tss, bs = ‘tp’) | 481.38 | 0.41 |
| mod5 | s(nh, bs = ‘tp’) + te(nh, tss, bs = c(‘tp’, ‘tp’)) | 481.83 | 0.41 |
| mod6 | s(tss, bs = ‘tp’) + te(nh, tss, bs = c(‘tp’, ‘tp’)) | 478.98 | 0.41 |
| mod7 | s(nh, bs = ‘tp’) + s(tss, bs = ‘tp’) + te(nh, tss, bs = c(‘tp’, ‘tp’)) | 479.77 | 0.41 |
Summary stats of best three three models:
# best model with season, year, flow
best3 <- map(mods3, ~ summary(.x)$r.sq) %>%
unlist %>%
which.max %>%
mods3[[.]]
best <- list(best1 = best1, best2 = best2, best3 = best3)
# smoother stats of GAMs
map(best, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | smoother | edf | Ref.df | F | p.value |
|---|---|---|---|---|---|
| best1 | s(dec_time) | 1.00 | 1.00 | 10.64 | 0.00 |
| best1 | s(doy) | 4.16 | 8.00 | 5.16 | 0.00 |
| best1 | te(dec_time,doy) | 2.85 | 15.00 | 0.28 | 0.16 |
| best2 | s(dec_time) | 1.00 | 1.00 | 1.93 | 0.17 |
| best2 | s(doy) | 2.94 | 8.00 | 0.71 | 0.05 |
| best2 | s(flo) | 6.78 | 7.86 | 2.96 | 0.00 |
| best2 | te(flo,doy) | 2.96 | 12.00 | 0.58 | 0.01 |
| best2 | te(flo,dec_time) | 0.21 | 15.00 | 0.02 | 0.09 |
| best2 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.81 |
| best2 | te(dec_time,doy,flo) | 19.86 | 48.00 | 1.01 | 0.00 |
| best3 | s(dec_time) | 8.05 | 8.73 | 2.78 | 0.00 |
| best3 | s(doy) | 4.40 | 8.00 | 5.36 | 0.00 |
| best3 | s(flo) | 1.00 | 1.00 | 5.66 | 0.02 |
| best3 | te(flo,doy) | 0.98 | 15.00 | 0.12 | 0.02 |
| best3 | te(flo,dec_time) | 3.94 | 16.00 | 1.21 | 0.00 |
| best3 | te(dec_time,doy) | 0.00 | 15.00 | 0.00 | 0.60 |
| best3 | te(dec_time,doy,flo) | 4.37 | 48.00 | 0.15 | 0.02 |
| best3 | s(nh) | 3.62 | 4.51 | 5.90 | 0.00 |
| best3 | te(nh,tss) | 9.82 | 20.00 | 1.52 | 0.00 |
# summary stats of GAMs
map(best, ~ data.frame(
AIC = AIC(.x),
R2 = summary(.x)$r.sq)) %>%
enframe %>%
unnest %>%
kable(digits = 2)| name | AIC | R2 |
|---|---|---|
| best1 | 608.68 | 0.17 |
| best2 | 556.83 | 0.34 |
| best3 | 481.83 | 0.41 |
# predictions
sl_res3 <- map(best, function(x){
sl_mod %>%
mutate(
pred = predict(x)
)
}) %>%
enframe('mods') %>%
unnest
# plot
p <- ggplot(sl_res3, aes(x = date)) +
geom_point(data = sl_mod, aes(y = chl), size = 0.5) +
geom_line(aes(y = pred, colour = mods)) +
theme_bw() +
theme(
legend.position = 'top',
legend.title = element_blank()
)
ggplotly(p)